1

Long-range p-d exchange interaction in a ferromagnet-semiconductor hybrid

structure

V.L. Korenev1,2,*, M. Salewski2, I.A. Akimov1,2,*, V.F. Sapega1,3, L. Langer2, I.V. Kalitukha1,

J. Debus2, R.I. Dzhioev1, D.R. Yakovlev1,2, D. Müller2, C. Schröder4, H. Hövel4,

G. Karczewski5, M. Wiater5, T. Wojtowicz5, Yu.G. Kusrayev1, and M. Bayer1,2

1Ioffe Physical-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia

2Experimentelle Physik 2, Technische Universität Dortmund, D-44227 Dortmund, Germany

3Physical Faculty of St. Petersburg State University, 198504 St. Petersburg, Russia

4Experimentelle Physik 1, Technische Universität Dortmund, D-44227 Dortmund, Germany

5Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland

Hybrid structures synthesized from different materials have attracted considerable attention

because they may allow not only combination of the functionalities of the individual constituents

but also mutual control of their properties. To obtain such a control an interaction between the

components needs to be established. For coupling the magnetic properties, an exchange

interaction has to be implemented which typically depends on wave function overlap and is

therefore short-ranged, so that it may be compromised across the interface. Here we study a

hybrid structure consisting of a ferromagnetic Co-layer and a semiconducting CdTe quantum

well, separated by a thin (Cd,Mg)Te barrier. In contrast to the expected p-d exchange that

decreases exponentially with the wave function overlap of quantum well holes and magnetic Co

atoms, we find a long-ranged, robust coupling that does not vary with barrier width up to more

than 10 nm. We suggest that the resulting spin polarization of the holes is induced by an effective

p-d exchange that is mediated by elliptically polarized phonons.

PACS: 85.75.–d, 78.67.–n

*Corresponding author: korenev@orient.ioffe.ru, ilja.akimov@tu-dortmund.de

2

Exchange interactions are the origin for correlated magnetism in condensed matter with multiply-

faceted behavior such as ferro-, antiferro- or ferrimagnetism. In magnetic semiconductors (SCs),

the exchange occurs between free charge carriers and localized magnetic atoms [1, 2, 3, 4] and is

determined by their wavefunction overlap. To assess and control this overlap, hybrid structures

consisting of a ferromagnetic (FM) layer and a semiconductor quantum well (QW) are appealing

objects because they allow wavefunction engineering. Furthermore, the mobility of QW carriers

may not be reduced by inclusion of magnetic ions in the same spatial region.

More specifically, for a two-dimensional hole gas (2DHG, the p-system) in a QW the

overlap of the hole wavefunction with the magnetic atoms in a nearby ferromagnetic layer (the d-

system) is believed to result in a p-d exchange interaction [5, 6, 7, 8]. This exchange interaction

may cause strong coupling between the SC and FM spin systems [9], through which the

ferromagnetism of the unified system, as evidenced by its hysteresis loop, for example, can be

tuned. In particular, the 2DHG spin system becomes polarized in the effective magnetic field of

the p-d exchange [5, 8]. Recently [10], it was shown that additionally to this equilibrium 2DHG

polarization there is an alternative mechanism involving spin-dependent capture of charge

carriers from the SC into the FM. For ferromagnetic (Ga,Mn)As on top of an (In,Ga)As QW,

electron capture induces their spin polarization in the QW, representing a dynamical effect in

contrast to the exchange-induced equilibrium polarization.

Here we study a different FM/QW hybrid consisting of a Co-layer and a CdTe-QW, i.e. a

II-VI semiconductor, separated by a nanometer-thick barrier. Due to the negligible hole

tunneling, this hybrid combination shows mostly the quasi-equilibrium ferromagnetic proximity

effect due to the p–d exchange interaction between Co atoms and CdTe-heavy holes.

Surprisingly, however, the proximity effect, measured through the spin polarization of the heavy

holes in the QW, is almost constant over large distances up to 14 nm spacer width. In contrast, for

3

conventional p-d exchange via wavefunction overlap an exponential decay with barrier width

with a characteristic decay length of about a nanometer would be expected. This novel exchange

coupling effect is therefore truly long-range, which is highly advantageous because it is robust

with respect to hybrid interface variations. As possible origin of this long-range proximity effect

we suggest an effective p-d exchange interaction mediated by elliptically polarized phonons

emitted from the FM into the QW.

Ferromagnet-induced circular polarization of the QW photoluminescence

We study a set of gradient structures composed of a Co-layer, a (Cd,Mg)Te-spacer (cap), and a

CdTe-QW followed by another (Cd,Mg)Te-barrier that was grown on top of a (100)-oriented

GaAs substrate (see Fig.1a for a general design of the structures). In the structure 1 the

(Cd,Mg)Te spacer was grown with the main shutter moving in front of the substrate in order to

have its thickness sd increasing continuously from 5 nm to 15 nm over a lateral structure

dimension of 5 cm (wedge shape). On top of this semiconducting sequence a 7 nm thick Co film

was deposited. The semiconducting parts of the other two structures are similar to those of

structure 1 except for the spacer thickness sd , which now was varied from zero to 10 nm and

from zero to 14 nm for structure 2 and 3, respectively, over 3 cm lateral dimension, followed by

an area with the constant thickness sd = 50 nm. Furthermore, for these samples, the Co film

thickness dCo varied in discrete steps of 1 nm from zero to 6 nm along the direction perpendicular

to spacer thickness gradient (Fig. 1a), followed by an area with the Co-film having constant

thickness of 16 nm. The Co layers are semitransparent for the exciting laser light. Atomic force

microscopy shows a non-uniform Co growth with islands having tens of nanometers lateral sizes

and height of about 5 nm (Fig. 1b). In the following we present the main experimental data for

4

structure 2 if not mentioned otherwise. We note that the main observations concerning the

proximity effect are similar for all structures.

The samples are illuminated with continuous or pulsed laser light, being either linearly ()

polarized or unpolarized through a depolarizing wedge. An out-of-plane magnetization

component can be induced by applying an external magnetic field in Faraday geometry BF

(longitudinal field parallel to the structure growth axis z||[001]). The band structure of the hybrid

system is sketched in Fig. 1c. For photon energies smaller than the band gap energy

2CdMgTegE eV of the barrier, only the QW is excited (Fig. 1a). The photoluminescence (PL)

emitted by the QW is analyzed with respect to its circular polarization + and , to determine the

circular polarization degree Fc B of the PL under -excitation.

Figure 1d shows half the difference c between the polarization degrees recorded for

FB +10 and 10 mT (blue dots) at T = 2 K for a spacer thickness of sd 10 nm in comparison

with a PL spectrum (black line). Further on we will often use the polarization difference

2/][)( FcFcFc BBB as a measure of the field-induced signal. Two main lines

centered at 1.63 eV (X-line) and ~1.60 eV (eA0 -line) with a wide flank towards lower energies

contribute to the PL. We assign the X-line to the heavy-hole exciton transition of the QW. The

eA0 line, on the other hand, is associated with electrons recombining with holes bound to

acceptors. This assignment is supported by time-resolved PL data, where the X-line decays

within 50 ps while the eA0 PL is observed during much longer times of nanoseconds (Fig. 2a).

From the typical exciton binding energy of 10 meV and the 20-30 meV distance between the two

lines one deduces a binding energy of 0AE 30-40 meV, which agrees well with the values for a

hole bound to a shallow acceptor in CdTe [11]. The degrees of circular PL polarization Fc B

5

vary considerably for FB = +10 and 10 mT (Fig. 1d) with a maximum difference at the eA0

line. A photoluminescence excitation spectrum reveals no strong dependence of Fc B on the

laser photon energy in the range of photon energies from 1.62 - 1.69 eV. Figure 1e shows the

magnetic field dependence of Fc B for excitation at exch 1.69 eV and detection at

PLh 1.59 eV. Up-and-down magnetic field scans show a non-hysteretic dependence of

Fc B saturating at a field strength of || satB 20 mT with a polarization amplitude

satc BA 4%, being an order of magnitude larger than without Co-layer (see

Supplementary Figure S3c). Fig. 1e also shows the dependence Fc B detected at

PLh 1.494 eV, corresponding to the eA0 PL transition from the GaAs substrate (the red

triangles). In contrast to the QW emission, we observe a much smaller polarization degree

without any saturation. Therefore the PL polarization from the CdTe QW is clearly induced by

the FM. We stress that magnetic circular dichroism in the FM layer and diffusion of magnetic

atoms into the QW region cannot cause the spin polarization (see Supplementary Section A; the

origin of the ferromagnet responsible for the polarization of the QW PL is discussed in

Supplementary Section B).

Time-resolved PL (TRPL) gives insight into the kinetics of the spin polarization after

linearly polarized excitation. Spectrally resolved intensity transients are shown in Fig. 2a. Figure

2b shows the temporal dependence of the FM-induced half the difference tc between

circular PL polarizations in magnetic fields of +40 mT and 40 mT, applied in Faraday

geometry: tc continuously increases with time: initially being non-polarized, the photo-

excited carriers acquire spin polarization with a characteristic rise time of fm 2 ns, obtained

from exponential fit (dashed line). In combination with the decay times of 50 ps for the X line

6

and a few nanoseconds for the eA0 line this allows one to explain the absence of polarization for

the X-line: the exciton does not live long enough to acquire polarization from the FM (another

possibility will be discussed below).

To understand the origin of the FM-induced PL polarization from the QW we have to

address the following questions: (i) Are the QW electrons or holes polarized? (ii) Does the spin-

dependent capture of carriers from the QW into the FM play a role? (iii) Is there an effective

exchange magnetic field from the FM polarizing the QW carriers?

(i) Ferromagnet-induced spin polarization of the QW heavy holes

As discussed, application of a longitudinal magnetic field FB causes a polarization of the PL.

Now we apply an additional magnetic field VB in Voigt geometry with the goal to depolarize the

FM-induced PL polarization (see scheme in Fig. 3a). Figure 3b shows that for 4FB mT the

half polarization difference c of the QW PL is about 1% and is not sensitive to the magnetic

field VB up to 20 mT. This means that the out-of-plane zM component of the FM remains fixed

in this range of Voigt-fields. However, this is not the only consequence. The data also indicate

heavy hole polarization as source of the non-zero c . Indeed, if c would arise from electron

spin orientation, the Hanle effect [12] should be observed for the electron spins. Electrons spins

are polarized along the z-axis, and the magnetic field VB induces Larmor precession about VB .

The frequency of precession should decrease the z-component of the electron spin, leading to a

PL depolarization Vc B in complete analogy with the Hanle effect under optical injection of

the electron spin. Indeed, under circularly polarized excitation the degree of polarization Vc B

decreases with VB (green solid circles in Fig. 3c) with a halfwidth 2/1B 15 mT. However, such

7

a dependence is absent for Vc B in the same field range (Fig. 3b). Moreover, Fig. 3c also

shows (the magenta triangles) that application of 4 mT longitudinal field does not change the

Hanle curve. It means that the magnetization of the FM does not create a noticeable magnetic

field (e.g., due to s-d exchange) which would influence the Larmor precession of the electron

spin. Therefore, the out-of-plane magnetization zM of the FM does neither orient electron spins,

nor does it affect their Larmor precession frequency. We conclude that the FM-induced

polarization c is directly related to the spin polarization of heavy holes: the in-plane g-factor of

heavy holes is close to zero, so that the VB field cannot depolarize them.

TRPL data allow one to determine the electron and hole spin dynamics for comparison

with the ~1 ns kinetics of the proximity effect. The bottom panel of Fig. 2c shows the optical

orientation signal 2,, tBtBt FcFcc at FB =40 mT, averaged over the magnetic

field direction, to exclude any contribution of the FM-induced polarization. One finds two decay

components with strongly different spin relaxation times se and sh . The shorter one

sh 0.12 ns corresponds to holes, whereas the much longer time se 20 ns corresponds to

electrons [10]. It is important to note that the zero-field decay of tc in Fig. 2c contains an

additional contribution 3.0deph ns due to electron spin dephasing in the randomly oriented

stray fields ~15 mT of the FM. The stray fields also determine the 15 mT width of the Hanle

curve (Supplementary Section A2). This dephasing affects the spin dynamics and leads to the

faster decay of tc at BF = 0. Application of a 40FB mT Faraday-field suppresses the stray

field impact. The comparison of mT 40, Fc Bt with the kinetics tc shows that the FM-

induced polarization kinetics is much faster ( fm 2 ns) than the electron spin kinetics

se 20 ns in agreement with the hole spin flip being much faster than that of the electron [12].

8

However, it is considerably slower than the hole spin-flip time of sh 0.15 ns. This faster spin

relaxation of the optically orientated holes can be explained by the higher laser photon energy

(1.70 eV) by which free holes are excited. The optically excited hot holes become depolarized

before they are trapped by acceptors.

Here we want to recall the unusual proximity effect shown in Fig. 1d: only the e-A0

transition shows a FM-induced polarization. Hence tc reflects the spin kinetics of the holes

bound to acceptors, whose spin-flip time can be considerably longer than sh . Further evidence

(Fig. 3d, upper panel) of the heavy hole polarization comes from the non-oscillating signal

mT 10, Fc Bt increasing with time in spite of the large magnetic field VB 96 mT applied

in Voigt geometry. In contrast, the optical orientation signal mTBt Fc 10, oscillates in time

according to the electron g-factor |ge|=1.2 and goes to zero (Fig. 3d, bottom panel).

We conclude that: 1) the out-of-plane magnetization component of the FM is robust in

magnetic fields VB <100 mT, and 2) the FM-induced PL polarization )( Fс B in longitudinal

field originates from the spin polarization of heavy-holes bound to acceptors.

(ii) Spin-dependent capture as possible source of non-equilibrium QW spin polarization

According to [10] the observed proximity effect may be due to spin-dependent carrier capture

from the semiconductor into the FM. In this case, the total PL intensity I (the sum of the right-

and left-handed circular PL components) in longitudinal magnetic field would depend on the

helicity of the exciting light. The intensity modulation parameter IIII

is essentially determined by the selection rules for the involved optical transitions hPi at the

laser energy h . According to [10], FciF BPB is equal to Fc B for heavy hole

9

exciton excitation when 1iP . Figure 4b shows the modulation parameter FB when the laser

photon energy was tuned to the X resonance at 1.62 eV and detected at the e-A0 transition (1.60

eV). FB is several times smaller than the polarization degree Fс B . In fact, FB is weak

over the whole range of laser energies 1.62-1.70 eV. We conclude that spin-dependent capture by

the FM is not the main source of the FM induced hole spin polarization.

(iii) Role of p-d exchange in spin polarization of QW heavy holes

Heavy hole spin polarization in the effective magnetic field of the p-d exchange interaction with

the magnetic atoms was predicted in Ref. [5]. The equilibrium polarization of the holes, when the

FM magnetization is saturated ( sMM ), obeys the Curie law for non-degenerate statistics

Tk

ME

NN

NNTP

B

sexs 22/32/3

2/32/3

. (1)

Here kB is the Boltzmann constant, sex ME is the spin splitting of the heavy holes in the FM

exchange field, 2/32/3 NN is the concentration of QW heavy holes with momentum projection

2/32/3 onto the growth direction and we assume that 1TPs . One can expect from

Eq.(1) that the hole spin polarization decreases with increasing T. The experiment confirms this

tendency (Fig. 4a). An estimation for T = 10 K shows that a few percent spin polarization

corresponds to the splitting exE of about 50 eV.

The p-d exchange from the overlap of the QW holes and Co d-shells is expected to scale

like 0exp~ dddE ssex due to wavefunction penetration through the rectangular potential

barrier. The same exponential behavior holds for the tunneling rate with the characteristic barrier

width hmd 220 which is less than 1 nm for the heavy holes mass 01.0 mmh and the

barrier height = 0.1 eV. Thus the two possible coupling effects discussed above are definitely

10

expected to be short-range. At first sight, this is in agreement with the steep decrease of PL

intensity due to carrier tunneling from the QW into the Co with decreasing barrier thickness (red

squares Fig. 1f), from which we find 0d =1.6 nm. However, the spin polarization does not follow

a similar steep decrease at all. The green circles in Fig. 1f show that sс d at FB 40 mT is

roughly constant and almost independent of sd . Furthermore and maybe even more surprising,

the proximity effect observed in our case is long-ranged and persists over more than 14 nm, in

contrast to our expectation from wavefunction overlap.

It should be noted that in other systems than the one studied here a long-range proximity

effect may occur, e.g. due to the spin-dependent capture by the FM. Previously this effect was

observed in a ferromagnetic GaMnAs/QW hybrid for electrons, and not for holes [10]. The

individual capture rates of electrons with spin up (down) have also an exponential

tunneling rate through the nonmagnetic spacer. The non-equilibrium polarization in the QW,

however, is determined by the ratio / , so that the exponential dependence is cancelled. Here

the spin dependent capture is weak in absolute terms, as it is related to holes, and the proximity

effect comes mainly from the p-d exchange interaction. Therefore we can conclude that our

results indicate a novel long-range – mechanism of p-d exchange coupling.

Origin of long-range p-d exchange coupling

In the following we discuss three possibilities for the observed long-range coupling: a)

magnetization of holes by the stray fields of the FM film; b) resonant tunneling through deep

centers in the CdMgTe spacer; c) spin polarization of holes by elliptically polarized phonons

emitted from the FM towards the QW.

a. Effect of FM stray magnetic fields on spin polarization of charge carriers

11

It is known that stray magnetic fields created in a SC by a nearby FM [13, 14] can have large

penetration depths and lead to dephasing (with characteristic time deph ) of electron spin Larmor

precession (Fig. 3d). The stray field averaged over a region much larger than the size of a

magnetic domain is ~4 LdM Cos 0.02 mT for a Co film thickness Cod 5 nm and a sample size

of L 5 mm. The hole spin polarization in a field of this strength is negligible. Larger local stray

fields wdM Cos4~ appear on length scales comparable with the domain size w. The stray field

measured by optical orientation is about 20 mT (Supplementary Section A2) and cannot provide

a notable spin polarization. Therefore stray fields cannot explain the observed hole spin

polarization.

b. Resonant tunneling through deep centers in the (Cd,Mg)Te spacer

Another possible reason is related to resonant transfer of spin coupling through overlapping

paramagnetic deep centers in the (Cd,Mg)Te barrier. Assuming a localization radius of the center

of about ~ta 1 nm one can estimate the concentration required to make such a coupling efficient

to be 213t 10~1~ aNt cm-3. Such a large concentration of paramagnetic centers was never

reported for (Cd,Mg)Te. Moreover, its presence should significantly affect the Larmor precession

frequency of the CdTe QW electrons, which was not observed. Therefore we consider this

possibility as highly unlikely (see also Supplementary Section A3).

c. Spin polarization of holes by elliptically polarized phonons

The long-range p-d exchange between FM and SC may be mediated by elliptically polarized

phonons generated in the ferromagnetic layer. Below we consider acoustic phonons as an

example. Coupling with elliptically polarized optical phonon modes [15] is discussed in

Supplementary Section C. Phonons propagating through a FM along the magnetization direction

m = M/Ms are elliptically polarized due to the strong hybridization of the acoustic phonon (linear

12

in momentum) and spin wave (quadratic in momentum) modes near the crossing points of their

dispersions, i.e. for a phonon-magnon resonance [16]. There are two crossing points at

frequencies of 101 10~ s-1 and 12

2 10~ s-1 with two orthogonal phonon polarizations per

crossing [16]. Only the phonon mode with polarization vector rotating in the same direction as

the magnetization vector in the spin wave participates in the coupling, while the other one

couples only weakly to magnons [17]. The elliptically polarized phonons transfer angular

momentum through the FM.

We suggest that such elliptically polarized phonons can affect the hole spin system when

transmitted through the interface between FM and SC with not too different acoustic impedances.

In this case elliptically polarized acoustic modes will propagate and hit the QW influencing the

confined hole spins, which resembles a proximity effect for phonon angular momentum. The

effect may obviously occur over much larger spacer thicknesses than any wavefunction overlap-

based mechanism because there is no energy barrier for phonons. Any hole spin-phonon coupling

is expected to change the energy of the heavy hole spin subbands due to the strong spin-orbit

interaction in the valence band. To the best of our knowledge this effective p-d exchange

coupling has not been discussed previously in literature and may be considered as phonon analog

of the ac Stark shift well known in optics [18], in which the action of circularly polarized

electromagnetic wave in a medium is equivalent to an effective magnetic field.

Let us discuss the effect in a bit more detail by assuming an elliptically polarized

transverse phonon that propagates along M (axis z ]001[ ) so that the angular momentum of the

phonon is parallel to M. Furthermore, we assume for illustrational purposes that only the phon

polarized phonon mode exists and propagates through the FM-SC interface (Fig. 5). The

interaction of the hole spin with this rotary lattice oscillation couples the ground state N,23

13

of the 23 heavy hole in the quantum well in presence of N phonons with the excited state

1,21 N of 21 light holes in the presence of N1 phonons, conserving thereby angular

momentum (see Supplementary Section C for details). This leads to the “phonon ac Stark effect”

– a spin-dependent shift of hole spin levels. The shift will be the stronger the closer the phonon

energy hk is to heavy-light hole spin splitting h (energy level diagram in Fig. 5). The

energy shift 23E will be different for the 2/3 levels. This dynamic, phonon-mediated

interaction induces therefore an effective p-d exchange coupling between FM and QW, which

can be written as

zzeffpd

eff mJV 2

1

(2)

with the Pauli matrix z in the basis of heavy-hole states 23 , and effJ being the effective p-d

exchange constant. The calculation of the “phonon ac Stark shift” of the QW hole levels requires

precise knowledge of many quantities - the interaction parameters, phonon propagation

directions, etc. - and is beyond the scope of the present work. However, we expect that the hole

spin polarization changes sign under reversal of zM , and the splitting 2323 EEEex

becomes larger for heavy-light hole splittings h 21, 1 meV. Correspondingly, the

splitting exE is expected to be larger for the acceptor bound holes A0 with ~Ah 1 meV [19],

than for the free QW holes with ~freeh 10 meV. This is another possible explanation for detection

of the proximity effect at the e-A0 transition and not at the X transition. The absence of a FM-

induced spin splitting of QW electrons (and the related precession corresponding to the Larmor

frequency) can be also explained by the small spin-orbit interaction in the conduction band.

All the discussed features are qualitatively consistent with the experimental data.

Therefore we come to the following basic conjecture: the long-range p-d exchange coupling is

14

mediated by elliptically polarized phonons. A direct observation of elliptically polarized phonons

in semiconductors could have profound consequences for the physics of spin systems in general,

and not only for hybrids. Firstly, it could enable one to control the spin levels through the phonon

analog of the optical ac Stark effect [18]. Secondly, one could show phonon-assisted spin

pumping: the absorption of circularly polarized phonons would create spin orientation of holes in

the valence band, similar to the well-known interband optical pumping in solids [20] and gases

[21].

Acknowledgments:

We acknowledge support by the Deutsche Forschungsgemeinschaft and Russian Foundation for

Basic Research in the frame of the ICRC TRR 160, the Government of Russia via project

N14.Z50.31.0021, and the Program of Russian Academy of Sciences. V.L.K. acknowledges the

Deutsche Forschungsgemeinschaft financial support within the Gerhard Mercator professorship

program. The research in Poland was partially supported by the National Science Center (Poland)

under grants nos. DEC-2012/06/A/ST3/00247 and DEC-2014/ST3/266881. T. W. acknowledges

also the support from the Foundation for Polish Science through the International Outgoing

Scholarship 2014.

Additional information

The authors declare no competing financial interests.

15

-50 -25 0 25 50-6

-4

-2

0

2

4

6

e-A0

GaAs

Circ

ular

pol

ariz

atio

n c (

%)

Magnetic field BF (mT)

6 8 10 12 140.1

1

Intensity Amplitude

Inte

nsi

ty (

arb

. uni

ts),

Am

plitu

de

(%)

Spacer thickness dS

(nm)

~exp(dS/d

0)

d0=1.6nm

z

x

y

3.2 m CdMgTe (Mg 20%)on GaAs substrate

10nm QW

`

50mm

ABCDE1

23

45

Cap

excitation

PL

BF

CoSpacer

QWBarrier

GaAssubstrate

Fermi level

1.56 1.58 1.60 1.62 1.640.0

0.5

1.0

1.5

Inte

nsi

ty (

arb.

uni

ts)

Photon energy hPL

(eV)

-1

0

1

2

3

4

5e-A0

Diff

eren

ce c

(%

)

Xfed

cba

Figure 1. Ferromagnetic-induced proximity effect. (a) Scheme of optical excitation of double

gradient structure 2. (b) AFM image of structure 2 with Co film thickness dCo = 5 nm . (c) Band

structure of investigated structures. Violet arrow indicates the excitation energy, while green and

red arrows correspond to PL from QW and GaAs substrate, respectively. (d) PL spectrum (black

line) and half the difference c = [c

(+BF) c(BF)]/2 (blue dots) between circular

polarizations c measured for BF = 10/+10 mT at T = 2 K, linearly polarized pulsed excitation

with photon energy 1.69 eV and excitation density 20 W/cm2. The spacer thickness sd =10 nm

and Co thickness Cod = 4 nm; (e) The dependence Fc B detected at the lower energy flank of

e-A0 transition from the QW around 1.59 eV as it is indicated with vertical arrow in panel (d)

(green circles) and GaAs substrate at 1.49 eV (red triangles); up-down field scan revealed no

hysteresis. (f) Dependence of exciton PL intensity on spacer thickness sd for dCo = 4 nm (red

squares). Dashed line is an exponential fit exp(-ds/d0) with characteristic length 0d =1.6 nm. Open

circles compare the spacer dependence of the proximity effect amplitude A mT 40Fc B ,

which appears to be constant.

16

-500 0 500 1000 1500 20000

5

10

15

20

1.57

1.58

1.59

1.60

1.61

1.62

1.63

c

b

Ph

oton

en

erg

y (e

V)

1.000 10.82 117.0 385.0

0

3

6

Diff

ere

nce

c (%

)

|BF| = 40mT

fm

~ 2 ns, A =6.5%8

sh

= 120ps, se

> 20ns

BF = 0

Time (ps)

Circ

ular

pol

ariz

atio

n c

(%

)

|BF|=40mT

a

Figure 2: Time-resolved spin dynamics. (a) Contour plot of PL intensity decay from the

QW. The frame indicates the region of interest for polarization measurements which corresponds

to eA0 transition. (b) Dynamics of FM induced proximity effect. Time evolution of half the

difference of circular polarization degree c = [c

(+BF) c(BF)]/2 for FB 40 mT under

linear polarized excitation is shown. Dashed line is a fit with )]exp(1[ fmc -t/τ-At with

fm 2 ns and A = 6.5%; (c) Optical orientation kinetics. Circular polarization under excitation

by -light 2,, tBtBt FcFcc are shown for |BF| = 40 mT and BF = 0. Red

dashed line results from double exponential fit of the data for |BF| = 40 mT with

)/exp()/exp( ,0,0 seeshhc ttt , where %7,0 h , sh =0.12 ns, %5.11,0 e at

|BF| = 40 mT and se > 20 ns.

17

BFBV

+

zx

y

Excitation PL

QW

0 500 1000 1500 2000

0

5

10

15

0

1

2

BF = 0

|BF| = 10 mT

Circ

ular

pol

aria

tion c

(%

)

Time (ps)

|BV| = 96 mT

|ge| = 1.2

|BF| = 10 mT

Diff

eren

ce

c>

(%)

|BV| = 96 mT

-20 -10 0 10 20

2

3

4

5

BF = 0

BF = + 4mT

ds = 7.4 nm

Circ

ular

pol

ariz

atio

n c (

%)

Voigt magnetic field BV (mT)

-20 -10 0 10 200.0

0.5

1.0

1.5

2.0

ds = 7.3 nm |B

F| = 4 mT

Diff

ere

nce

c (

%)

Voigt magnetic field BV (mT)d

b

c

a

Figure 3. Ferromagnetic-induced spin polarization of the QW heavy holes bound to

acceptors. (a) Sketch of the experiment in crossed magnetic fields. (b) Sample 1. Dependence

Vс B in magnetic field in Voigt geometry in the presence of a longitudinal field 4|| FB mT.

(c) Hanle effect Vс B in the absence of the longitudinal field (green circles) and in the

presence of FB = +4 mT (magenta triangles). (d) Sample 2, ds = 10 nm. Upper panel: Kinetics of

2/],,[ VсVсс BtBtt of proximity effect at |BV| = 96 mT, FB 10 mT.

Bottom panel: Kinetics tс

of optical orientation in magnetic field |BV| = 96 mT, 0FB

(green circles), FB 10 mT (magenta triangles). Dashed line is the fit with

CtBgttt VBedepheshhc )/cos()/exp()/exp( ,0,0 with %8,0 h , sh =0.15 ns,

%5,0 e , |ge|=1.2, 1deph ns, C=1.5%. T = 2 K.

18

0 5 10 15 20 25 300

1

2

3

4

Am

plitu

de A

(%

)

Temperature (K)

BF = 100 mT

-100 -75 -50 -25 0 25 50 75 100

-1

0

1

T = 4 K

c

Inte

nsity

mo

dula

tion,

Circ

ula

r po

lariz

atio

n c

(%

)

Magnetic Field BF (T)

-1

0

1

b

a

Figure 4. Effective p-d exchange interaction between FM and QW heavy holes. (a)

Temperature dependence of the saturation amplitude in sample 1. (b) Sample 1. Resonant

excitation of exciton (1.619 eV), detection e-A0 (1.602 eV). The dependence of intensity

modulation parameter FB (red squares, right axis, laser with alternate helicity without

polarizers in the detection channel) is compared with FM-induced polarization Fc B (blue

circles, left axis, - excitation).

19

Figure 5. Illustration of circularly polarized phonon mode in the FM-QW hybrid structure.

Energy diagram: a circularly polarized phonon couples the ground state of heavy hole and the

excited state of light hole inducing spin-dependent shift of hole spin levels – “phonon ac Stark

effect”.

20

References

1. Kittel, C. Introduction to Solid State Physics, 3rd ed. (Wiley, New York,1967).

2. Furdyna, J. K. Diluted magnetic semiconductors. J. Appl. Phys. 64, R29-R64 (1988).

3. Dietl, T. A ten-year perspective on dilute magnetic semiconductors and oxides. Nature Mater.

9, 965-974 (2010).

4. Nagaev, E. L. Photoinduced magnetism and conduction electrons in magnetic semiconductors.

Physica Status Solidi B 145, 11 (1988).

5. Korenev, V. L. Electric control of magnetic moment in a ferromagnet/semiconductor hybrid

system. JETP Lett. 78, 564 (2003).

6. Myers, R. C., Gossard, A. C. & Awschalom, D. D. Tunable spin polarization in III-V quantum

wells with a ferromagnetic barrier. Phys. Rev. B 69, 161305(R) (2004).

7. Zaitsev, S. V. et al. Ferromagnetic effect of a Mn delta layer in the GaAs barrier on the spin

polarization of carriers in an InGaAs/GaAs quantum well. JETP Lett. 90, 658-662 (2010).

8. Pankov, M. A. et al. Ferromagnetic transition in GaAs/Mn/GaAs/InxGa1−xAs/GaAs structures

with a two-dimensional hole gas. JETP 109, 293-301 (2009).

9. Zakharchenya, B. P. & Korenev, V. L. Integrating magnetism into semiconductor electronics.

Physics Uspekhi 48, 603 (2005).

10. Korenev, V. L. et al. Dynamic spin polarization by orientation-dependent separation in a

ferromagnet-semiconductor hybrid. Nature Commun. 3, 959 (2012); doi: 10.1038/ncomms1957

11. Crowder B. L., & Hammer, W. N. Shallow acceptor states in ZnTe and CdTe. Physical

Review 150, 541-549 (1966).

12. Meier F. & Zakharchenya B. P., editors. Optical Orientation. (North Holland Publishing

Company, Amsterdam 1984).

21

13. Dzhioev R. I., Zakharchenya, B. P., & Korenev, V. L. Optical orientation study of thin

ferromagnetic films in a ferromagnet/semiconductor structure. Physics of the Solid State 37,

1929-1935 (1995).

14. Korenev, V. L. Optical orientation in ferromagnet/semiconductor hybrids. Semicond. Sci.

Technol. 23, 114012 (2008).

15. Schaack, G. Observation of circularly polarized phonon states in an external magnetic field.

J.Phys.C: Solid State Physics 9, L297-L301 (1976).

16. Kittel, C. Interaction of spin waves and ultrasonic waves in ferromagnetic crystalls. Phys.

Rev. 110, 836-841 (1958).

17. Tucker, J.W. & Rampton, V.W. Microwave Ultrasonics in Solid State Physics (North

Holland, Amsterdam, 1972).

18. Cohen-Tannoudji, C. & Dupont-Roc, J. Experimental study of Zeeman light shifts in weak

magnetic fields. Phys.Rev. A 5, 968-984 (1972).

19. Sapega, V. F., Ruf, T., Ivchenko, E. L., Cardona M., Mirlin, D. N. & Ploog, K. Resonant

Raman scattering due to bound-carrier spin-flip in GaAs/AlxGa1-xAs quantum wells, Phys.Rev.B

50, 2510 (1994).

20. Lampel, G. Nuclear Dynamic polarization by optical electronic saturation and optical

pumping in semiconductors. Phys. Rev. Lett. 20, 491-493 (1968).

21. Kastler, A. Nobel lecture 1966, Optical methods for studying Hertzian resonances, in Nobel

Lecture Physics 1963-1970 (World Scientific, Singapore, 1998) p.186.

1

Supplementary information

Long-range p-d exchange interaction in a ferromagnet-semiconductor hybrid

structure

V. L. Korenev1,2, M. Salewski2, I. A. Akimov1,2, V. F. Sapega1,3, L. Langer2, I. V. Kalitukha1,

J. Debus2, R. I. Dzhioev1, D. R. Yakovlev1,2, D. Müller2, C. Schröder4, H. Hövel4,

G. Karczewski5, M. Wiater5, T. Wojtowicz5, Yu. G. Kusrayev1, and M. Bayer1,2

1Ioffe Physical-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia

2Experimentelle Physik 2, Technische Universitat Dortmund, D-44227 Dortmund, Germany

3Physical Faculty of St. Petersburg State University, 198504 St. Petersburg, Russia

4Experimentelle Physik 1, Technische Universitat Dortmund, D-44227 Dortmund, Germany

5Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland

2

A. Origin of the ferromagnet-induced QW PL circular polarization.

Here we discuss more possibilities of FM-induced circularly polarized emission from the QW.

We show that these alternative mechanisms cannot explain the experimental data.

A1. Effect of magnetic circular dichroism.

We can exclude any potential influence from magnetic circular dichroism (MCD), i.e., the

dependence of the absorption coefficient on photon helicity. MCD would induce a PL

polarization even if the carriers in the QW would be non-polarized. To check, detection was

done at the e-A0 PL transition (1.494 eV) of the GaAs substrate, and the laser was scanned with

alternating helicity across the QW resonances in the range from 1.59 to 1.63 eV with a Faraday-

field of FB 70 mT applied. Only negligible changes of the PL intensity <0.3% were found.

Therefore MCD is not important and the observed A 4% polarization results from the

ferromagnet-induced spin polarization of two-dimensional electrons and/or holes.

A2. Role of stray fields in the FM-induced spin polarization.

Optical orientation of electrons occurs under excitation by circularly polarized light. The

dependencies of the circular polarization degree Bc on magnetic field in Voigt geometry (the

Hanle effect) and in Faraday geometry (effect of stabilization of the optical orientation, recently

called the “inverted” Hanle effect [S1]) are determined by the distribution of magnetic stray

fields [S2]. The Hanle effect (Fig. S1) is the depolarization of PL in a magnetic field VB in Voigt

geometry and results from the electron spin precession about VB . The transversal hole g-factor is

close to zero so that the hole depolarization is negligible. The half-width of the depolarization

curve VB 2/1 15 mT in structure 1 for the 7-10 nm range of the spacer thickness. A magnetic

field in Faraday geometry increases the circular polarization (“inverted” Hanle effect) with a

similar characteristic field FB 2/1 30 mT. This behavior points towards the presence of stray

magnetic fields in the QW region due to the domain structure of the FM [S2] or interface

roughness [S1]. (Note that the fringe fields due to hyperfine interaction with the nuclei are about

3

0.5 mT in CdTe QW [S3] and can be safely neglected). The effect of the stray fields is also seen

in TRPL data, where they lead to a dephasing of the optical orientation of electrons with a

characteristic time 3.00.1*2 Tdeph ns, see the lower panel of Fig. 3d. For the case of an

isotropic distribution of the random fields there is a relation [S4] between VB 2/1 , FB 2/1 , and *2T :

*22/12/1 32 TgBB eB

VF . Taking into account | eg | = 1.2 one obtains mT 22/2/1 VFB , which is

between the VB 2/1 15 mT and FB 2/1 30 mT observed experimentally. The difference from

FV BB 2/12/1 indicates an anisotropic distribution of the FM random fields. Small local fields in

the ten mT range can affect the electron spin precession kinetics. However, the polarization of

electrons (and of holes whose longitudinal g-factor is similar) due to thermal distribution

between the spin sublevels at T = 2 K cannot exceed 0.5% at this field strength, i.e. is too small

to explain experiment.

A3. Role of diffusion of magnetic atoms into the QW region or of cluster formation

Diffusion of magnetic atoms into the QW region could enhance the effective Lande g-factors of

spins, so that 1effg , due to exchange interaction similar to the behavior in diluted magnetic

semiconductors. Another possibility for the small saturation field satB ~20 mT of Fc B (see

Fig. S2) could be superparamagnetic Co cluster formation. For clarification, the polarization

dependencies Fc B were measured at different temperatures in the range from 2 up to 30 K.

Figure S2 shows that all curves coincide when the measured amplitudes are scaled accordingly.

Therefore the polarization originates from a ferromagnet, and not from paramagnetic clusters or

Co impurities. In the latter cases, the saturation of Bc would depend on the ratio

TkBM Bc ( Bk is the Boltzmann constant, and cM is the magnetic moment of the cluster) or on

TkBg BeffB for Co impurities. With increasing temperature polarization saturation should

occur then in larger fields, TkTB Bsat ~ . However, the saturation of Fc B takes place at

satB =20 mT over the entire temperature range in Fig. S2. This also means that the

4

ferromagnetism of the Co layer is not sensitive to temperature up to 30 K (the origin of the

ferromagnetic behavior will be discussed below). The decrease of polarization with increasing

temperature (Fig. 4a) is related to the decreasing sensitivity of the “QW detector” to

ferromagnetism.

B. Origin of the ferromagnet responsible for the spin polarization of the QW holes.

The magneto-optical Kerr effect is often used to measure the magnetic hysteresis loop of thin

magnetic films. In our case, the Kerr data show that the magnetization of the Co film is oriented

in-plane due to demagnetization with the saturation field FB being about 1.5 T (see Fig. S3a),

which is a typical value for sM4 in Co. The magnetization by an in-plane magnetic field VB

perpendicular and parallel to the spacer gradient direction show magnetic hysteresis loops with a

coercivity 120cB mT (see Fig. S3b). No changes within the 20 mT accuracy can be seen in

Figs. S3a and S3b. These data are in contrast with the proximity effect: The PL polarization

degree c in perpendicular magnetic field FB saturates at FB 20 mT (Fig. 4b of the main text

and Fig. S1) and is weakly sensitive to an in-plane magnetic field with VB < 100 mT.

We conclude that the Kerr technique and the PL polarization technique detect

ferromagnets with different properties – the easy-plane for the former and the perpendicular

anisotropy for the latter method. The FM detected by the Kerr effect can be ascribed to the Co

film itself, whereas the other FM could be related to interfacial ferromagnetism with properties

differing substantially from the Co film. The interfacial FM layer is expected to be thinner than

the Co film thickness, so that it is hard to be seen by the Kerr technique. In contrast, the FM-QW

exchange coupling may be sufficient to induce spin polarization of nearby QW charge carriers.

Interfacial ferromagnetism was discovered in a Ni/GaAs hybrid [S2] and was discussed later in a

number of papers [S5, S6]. At this stage, the origin of the FM responsible for the proximity

effect in the Co/(Cd,Mg)Te/CdTe hybrids studied here needs further investigation in future.

Currently we can exclude Co-related oxides as origin because the structures 2 and 3 were grown

5

without exposure to air before FM sputtering. Therefore, possible origins are Co-(Cd,Mg)Te

intermixing and/or interfacial ferromagnetism. Interestingly, the FM proximity effect decreases

with increasing Co thickness. Figure B3 shows the time-integrated amplitude mT 40cA

versus the Co thickness Cod for a fixed spacer thickness nm 10sd at K 2T . The proximity

effect decreases not only for small Co thicknesses nm 4Cod (which is natural) but also for

nm 4Cod . The latter may be related to reorientation of the easy axis or change of the interfacial

ferromagnetism, when the Co film becomes thick enough.

C. Hole spin – phonon coupling in the semiconductor valence band

The interaction of the hole spin J with acoustic phonons through the shear strain is

described by the Hamiltonian [S7]

yxsxyyzsyzxzsxzhph JJJJJJd

H ,,,3

2

where 2/, zxxzsxz JJJJJJ , and the constant d has a typical value of about 10 eV. We

assume for simplicity that the Hamiltonian has no dependence on x, y. Therefore, the

components of the strain tensor z

Rxxz

2

1 , z

Ryyz

21 , 0xy . The x, y components of

the displacement vector are given by k

ikzk

ikzk

k

ebebR *

2

, where kk bb are the

creation (destruction) operators of a phonon with momentum k and frequency k , propagating

along the z axis, * is the complex -component of the polarization vector ξ

, is the

mass density of the crystal. The Hamiltonian takes a convenient form after transformation to the

ladder operators yx iJJJ and the circularly polarized basis

k

ikzkyx

ikzkyx

kyx ebiebiiRRR *

2

6

z

RJJ

z

RJJ

dH szszhph ,,

32 (C1)

The first term in Eq. (C1) couples the ground state N,23 of the heavy hole in the QW in

presence of N phonons to the excited state 1,21 N of light holes in presence of N-1

phonons with a probability amplitude NHN hph ,231,21 via a phon circularly

polarized phonon (coefficients 2,21 iyx ), in accordance with angular momentum

conservation. Similarly, the second term in Eq. (C1) couples the ground state N,23 of the

QW heavy hole in presence of N phonons and the excited light hole state 1,21 N in

presence of N-1 phonons with the probability amplitude NHN hph ,231,21 via a

phon

phonon. As the number of phonons with opposite circular polarizations is different especially

near the magnon-phonon resonance, the probability amplitudes for the two couplings

23 21 and 23 21 are different. Assuming that near the resonance only the phon

phonon mode survives, we obtain a splitting of the heavy-hole states due to the “phonon ac Stark

effect”

q hq

qhphq

ex

NHNE

2,231,21

, (C2)

where the sum is limited to wave vectors q, for which the dispersion relation of the transverse

acoustic phonons is close to the magnon-phonon resonance, ., 21 q It follows from

Eq.(C2) that the splitting 2323 EEEex is maximal when the energy of the magnon-

phonon resonance meV 1, 21 is close to h . For the acceptor the energy splitting

meV 1 h is indeed close to the phonon resonance, in contrast to the few ten meV energy

splitting between the free hole subbands. Therefore, the spin splitting of the 3/2 acceptor levels

is expected to be larger than that of the QW exciton, in accordance with the stronger polarization

for the e-A0 line. Using Eq. (C2) we can estimate the minimal strain component value to

7

produce a splitting μeV50 exE as estimated in experiment. One obtains

2

~ dEex ,

with a detuning h 2,1 from the magnon-phonon resonance. This gives 510~ for

d = 7 eV and = 0.1 meV. Such a small strain value can easily be obtained in semiconductors.

One cannot exclude the possibility of elliptically polarized transversal optical phonons

(corresponding to the zero-point motion in the low temperature case). Coupling with circularly

polarized optical phonons looks like spin-dependent polaronic shifts and can give a similar

splitting value for the free hole and for the hole bound to acceptor. Circularly polarized optical

phonons were observed in magnetic field (Ref. 15 of the main text). To illustrate this point we

consider for simplicity a crystal with two atoms per unit cell. Uniform strain is characterized by

the relative displacement 21 RRr of the sublattices 1 and 2. Unlike the acoustic phonon

case, optical oscillations do not shift the center of mass of the unit cell. Hence the spin-phonon

Hamiltonian includes the displacement itself, without derivatives with respect to the coordinates

(being typically much smaller)

sxyzzxysxzyyzxsyzxxyzhopt JJrQJJrQJJrQH ,,, (C3)

The third rank tensor Q̂ has only one independent component zxyyzxxyz QQQQ

(dimensionality eV/A) in CdTe-type bulk semiconductors. The order of magnitude of the

parameter is 20

2~ aeQ ~1 eV/A ( 0a is the linear size of the unit cell). Optical phonon modes

propagating along m

z (the structure growth axis) have angular momentum parallel to z. The

angular momentum is related to the x and y components of the displacement vector r. For this

reason we omit the last term in Eq. (C3). Similar to (C1) it is convenient to transform the

Hamiltonian (C4) to the operators yx iJJJ and the circularly polarized basis

k

ikzkyx

ikzkyxyx ebiebiirrr

*0000

02

where 0ξ

is the complex polarization

vector of the optical phonon, and 0 is its frequency. One obtains

8

szszhopt JJrJJri

QH ,,

2 (C4)

We consider the low-temperature case TkBh 0, , when only +3/2 heavy hole states are

populated and there are no optical phonons. The shift of the energy level of the +3/2 hole follows

from second-order perturbation theory

q h

qhoptq HE

0

2

2/3

0,231,21

, (C5)

where the matrix element in Eq. (C5) couples the ground +3/2 state without phonons with the

excited 2/1 hole state with one phonon q1 having momentum q along z and polarization

(the second term in (C4) is responsible for this coupling). The upper index in the phonon

frequency takes explicitly into account the time-reversal broken symmetry in the FM/SC hybrid,

so that the phonon energies 00 are different for and polarizations. Using

Eq. (C5) we obtain for a small splitting 000 of the phonon mode

002/32/3 EEEopt

ex (C6)

where the coefficient 101~ 20

2

hoptH . We do not know the difference

00 and the parameter for the studied hybrid. Taking as a reference point

00 20 cm-1 [15] and our estimation μeV50 exE one has 01.0~ . Finally we note

that the optical phonon energy 0 21 meV is larger than the h splitting for both the valence

band heavy hole (about 10 meV) and the hole bound to a shallow acceptor (about 1 meV). Hence

the splitting optexE will be comparable for both hole states in contrast to the case of interaction

with acoustic phonons (C2).

9

-50 -40 -30 -20 -10 0 10 20 30 40 500

2

4

6

8

10

12

14

Voigt

BV

1/2=15 mT

Faraday

BF

1/2=30 mT

Circ

ular

pol

ariz

atio

n,

c, %

2 mW

Magnetic field (mT)

Figure S1. Magnetic field dependence of circular polarization. Hanle effect (the circles) in

Voigt geometry, fitted with a Lorentzian with VB 2/1 15 mT. “Inverted” Hanle effect (the

squares), also fitted by a Lorentzian with FB 2/1 30 mT; T = 10 K, structure 1.

10

-20 -15 -10 -5 0 5 10 15 20-6

-4

-2

0

2

4

6

T (K) 2 10 15 20

C

ircul

ar p

olar

izat

ion c (

arb.

uni

ts)

Magnetic field BF (mT)

sample 1d

s=7.45nm

dC0

=7nm

Figure S2. Effective p-d exchange interaction between FM and QW heavy holes.

Dependence Fc B on magnetic field at different temperatures for a spacer thickness of 7.5 nm;

all curves are rescales to a single one by rescaling the vertical scale of the data to the same

average circular polarization value.

11

-0.4 -0.2 0.0 0.2 0.4

-0.8

-0.4

0.0

0.4

0.8B

incident

reflected

Ker

r ro

tatio

n (a

rb.

units

)

Magnetic field BV (T)

B

spacer gradient

0 5 10 150

1

2

3

4

5

6

Am

plit

ude

A (

%)

Co thickness dCo

(nm)

c

-3 -2 -1 0 1 2 3-60

-40

-20

0

20

40

60

-0.10 -0.05 0.00 0.05 0.10

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Ker

r ro

tatio

n (a

rb.

units

)

Magnetic field BF (T)

B

incident

reflected

Ke

rr r

ota

tion

(arb

.un

its)

Magnetic field BF (T)

b

a

Figure S3. (a) The polar Kerr effect reveals the out-of plane magnetization component in

Faraday field FB . (b) The longitudinal Kerr effect detects the in plane magnetization component

for two different VB field orientations, parallel and perpendicular to the spacer thickness

gradient. (c) Time-integrated amplitude mT 40 Fc BA versus Co thickness Cod for

sd 10 nm and T = 2 K.

12

References SOM

S1. Dash, S. P., Sharma, S., Le Breton, J. C., Peiro, J., Jaffrès, H., George, J.-M., Lemaître, A., &

Jansen, R. Inverted Hanle effect spin precession and inverted Hanle effect in a semiconductor

near a finite-roughness ferromagnetic interface. Phys. Rev. B 84, 054410 (2011).

S2. Dzhioev, R. I., Zakharchenya, B. P., & Korenev, V. L. Optical orientation study of thin

ferromagnetic films in a ferromagnet/semiconductor structure. Physics of the Solid State 37,

1929-1935 (1995).

S3. Zhukov, E. A., Yakovlev, D. R., Bayer, M., Glazov M. M., Ivchenko, E. L., Karczewski, G.,

Wojtowicz, T., & Kossut, J. Spin coherence of a two-dimensional electron gas induced by

resonant excitation of trions and excitons in CdTe/(Cd,Mg)Te quantum wells. Phys. Rev. B 76,

205310 (2007).

S4. Merkulov, I. A., Efros Al. L., & Rosen, M. Electron spin relaxation by nuclei in

semiconductor quantum dots. Phys. Rev. B 65, 205309 (2002).

S5. Nie, S.H. et al., Ferromagnetic interfacial interaction and the proximity effect in a

Co2FeAl/(Ga,Mn)As bilayer. Phys. Rev. Lett. 111, 027203 (2013).

S6. Wilson, M. J., Zhu, M., Myers, R. C., Awschalom, D. D., Schiffer, P. & Samarth, N.

Interlayer and interfacial exchange coupling in ferromagnetic metal/semiconductor

heterostructures. Phys. Rev. B, 81, 045319 (2010).

S7. Ivchenko, E.L., & Pikus, G.E. Superlattices and Other Heterostructures. Symmetry and

Optical Phenomena, Springer Series in Solid-State Sciences, vol. 110, (Springer-Verlag, Berlin,

Heidelberg , 1995).